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Let f be a germ of a holomorphic self-map of C 2 at the origin O tangent to the identity, and with O as a nondicritical isolated fixed point. A parabolic curve for f is a holomorphic f -invariant curve, with O on the boundary, attracted by O under the action of f . It has been shown by M. Abate (2001) that if the characteristic direction [v] ∈ P(T O C 2 ) has residual index not belonging to Q + , then there exist parabolic curves for f tangent to [v]. In this paper we prove, using a differentdoi:10.1090/s0002-9947-08-04533-9 fatcat:nbcgvro7cjakxfanxxqtjpmgru